Simplify the following expression: $ a = \dfrac{-9}{x + 1} - \dfrac{-7}{2} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{2}{2}$ $ \dfrac{-9}{x + 1} \times \dfrac{2}{2} = \dfrac{-18}{2x + 2} $ Multiply the second expression by $\dfrac{x + 1}{x + 1}$ $ \dfrac{-7}{2} \times \dfrac{x + 1}{x + 1} = \dfrac{-7x - 7}{2x + 2} $ Therefore $ a = \dfrac{-18}{2x + 2} - \dfrac{-7x - 7}{2x + 2} $ Now the expressions have the same denominator we can simply subtract the numerators: $a = \dfrac{-18 - (-7x - 7) }{2x + 2} $ Distribute the negative sign: $a = \dfrac{-18 + 7x + 7}{2x + 2}$ $a = \dfrac{7x - 11}{2x + 2}$